Aram says that the least common multiple of 4 and 6 is 24. Which is true about Aram’s statement?
a. 24 is a common multiple, but not the least common multiple
b.24 is not a common multiple of 4 and 6.
c.24 is the least common multiple.
d.24 is also the greatest common factor.
The Correct Answer and Explanation is:
Aram’s statement that the least common multiple (LCM) of 4 and 6 is 24 is incorrect. The correct answer is a. 24 is a common multiple, but not the least common multiple.
Explanation:
To understand why this is the correct answer, let’s first define what the least common multiple is. The LCM of two numbers is the smallest positive integer that is a multiple of both numbers.
Step 1: Identify the Multiples
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, …
- The multiples of 6 are: 6, 12, 18, 24, 30, …
Step 2: Find Common Multiples
From the lists above, we can see the common multiples of 4 and 6 are: 12, 24, 36, …
Step 3: Determine the Least Common Multiple
Out of the common multiples, the smallest one is 12. Thus, the LCM of 4 and 6 is 12, not 24.
Step 4: Analyze the Options
- Option a is correct because 24 is indeed a common multiple (it appears in both lists of multiples), but it is not the smallest.
- Option b is incorrect because 24 is a common multiple.
- Option c is incorrect because, as established, 12 is the LCM.
- Option d is incorrect because the greatest common factor (GCF) of 4 and 6 is 2, which is the largest number that divides both without a remainder.
In conclusion, while Aram correctly identifies 24 as a common multiple, he mistakenly claims it to be the least common multiple. Understanding the difference between common multiples, least common multiples, and greatest common factors is crucial in solving problems related to multiples and factors in mathematics.